NCERT Solutions

Maths - 12th Class

The NCERT solutions for class 12 maths provide a solid understanding of all the concepts that revolve around the CBSE NCERT Class 12 maths syllabus. Eduauraa NCERT solutions for class 12 maths cover all the important topics with chapter-wise solutions for all the exercises. The NCERT solutions provide students with the means to prepare for their examinations thoroughly. The solutions also help students to prepare for entrance examinations like JEE Mains, BITSAT, etc.


Eduauraa brings you the best Class 12 Maths NCERT Solution. Our solutions are designed by experts which help students with a smooth and accurate understanding of all formulas and concepts. These solutions for class 12 maths provide a detailed step-by-step explanation of all problems of the textbook. Besides the solutions, the Eduauraa solutions also have several exemplar problems, previous year questions, sample papers, and assignments that can help students to prepare for the board exams.

CBSE NCERT Solutions for Class 12 Maths Chapter-Wise:

Eduauraa provides free PDF format solutions that students can download from the website without any registration. Here is a chapter wise description of the NCERT Class 12 math notebook:

The Chapter include (Chapter-wise):

CHAPTER 01
Relations and Functions
CHAPTER 02
Inverse Trigonometric Functions
CHAPTER 03
Matrices
CHAPTER 04
Determinants
CHAPTER 05
Continuity and Differentiability
CHAPTER 06
Applications of Derivatives
CHAPTER 07
Integrals
CHAPTER 08
Electromagnetic Waves
CHAPTER 09
Applications of Integrals
CHAPTER 10
Differential Equations
CHAPTER 11
Three-dimensional Geometry
CHAPTER 12
Linear Programming
CHAPTER 13
Probability

Chapter 01: Relations and Functions



Chapter 1 of the NCERT maths textbook deals with relations and functions, types of relations, different types of functions, the function composition and invertible functions, binary operations, and several miscellaneous examples. There are four exercises that provide extensive problems for practice and understanding of the topics. The miscellaneous exercise also provides exclusive questions from topics like the inverse of functions, composite functions, symmetric, etc.


Chapter 02: Inverse Trigonometric Functions



The chapter provides several topics that are based on inverse trigonometrical functions and properties of inverse trigonometric functions. These concepts are well explained with several examples and exercises to practice. The chapter provides a vivid understanding of inverse trigonometry and helps students prepare for examinations including major entrance exams. The chapter is divided into two exercises and one miscellaneous exercise that has exclusive questions from Graphs of inverse trigonometric functions, properties of inverse trigonometry, etc.


Chapter 03: Matrices



Chapter 3 of the NCERT solutions for class 12 matrices deals with the definition of a matrix, types of matrices, equality of matrices, operation on matrices, the addition of matrices and multiplication of a matrix by a scalar, matrix addition, properties of multiplication, multiplication of matrices, properties of multiplication of matrices, transpose of a matrix, symmetric and skew-symmetric matrices, elementary operation or transformation of a matrix, and the inverse of a matrix by elementary operations. The textbook is also equipped with a miscellaneous exercise in addition to the four exercises in the chapter.


Chapter 04 : Determinants



Class 12 NCERT maths solutions chapter 4 discusses the topics of determinants. The students learn about the definition and meaning of determinants, finding the area of a triangle using determinants, minors of determinants, adjoint matrix, the inverse of a matrix, applications of determinants, and matrices. The textbook has 6 exercises and one miscellaneous exercise for students to practice and evolve their skills.


Chapter 05: Continuity and Differentiability



NCERT solutions for class 12 maths chapter 5 starts with the definition of continuity and provides students with the description of several topics like the algebra of continuous function, definition and meaning of differentiability, derivatives of composite functions, derivative of inverse trigonometric functions, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, and second-order derivatives. The chapter has eight exercises and a miscellaneous exercise that provides extensive questions from all the topics.


Chapter 06: Applications of Derivatives



This chapter deals with all definitions and concepts related to the rate of change of quantities, increasing functions, decreasing functions, tangents and normals, approximations, maxima and minima, first derivative test, and maximum and minimum values of a function in a closed interval. The chapter has five exercises and a miscellaneous exercise with exclusive questions for better preparation for the examinations.


Chapter 07: Integrals



The chapter about integrals involves the definition of indefinite integral, integration as an inverse of differentiation, geometrical interpretation of indefinite integral, properties of indefinite integral, differentiation and integration, methods of integration , integration using partial fractions, integration for trigonometric identities, integration of some integral functions, the meaning of definite integrals, definite integral as the limit of a sum, evaluation of definite integrals by substitution, and some properties of definite integrals. The chapter has 11 exercises that discuss and provide problems for practice.


Chapter 08: Applications of Integrals



The chapter for application of integrals discusses major topics of integrals including area under simple curves, area of the region in a curve and a line, and area between two curves. The chapter has two exercises and one miscellaneous example.


Chapter 09 : Differential Equations



The chapter on differential equations discusses major topics that include the degree of a differential, homogeneous differential equations, linear differential equations, order of a differential equation, general and particular solutions of a differential equation, the process to form a differential equation that represent a given family of curves, methods of solving first order, first-degree differential equations, differential equations with variable separable, and the procedure involved to solve first-order linear differential equations. The chapter discusses different forms of linear differential questions with 6 exercises that have extensive problems.


Chapter 10: Vector Algebra



This chapter deals with the introduction of vector algebra. The concepts in the chapter cover several topics including unit vector, multiplication of a vector by a scalar, vector components, vector joining two points, collinear vector, equal vector, negative of a vector, section formula, the product of two vectors, scalar or dot product of two vectors, properties of scalar product, projection of a vector on a line, and much more. The chapter has four exercises and one miscellaneous exercise that includes exclusive problems for practice.


Chapter 11: Three-dimensional Geometry



Chapter 11 of the NCERT maths textbook for class 12 constitutes several topics related to three-dimensional geometry. The chapter deals with direction cosines and direction ratios of a line, the relation between the direction cosines of a line passing through two points, equation of a line in space, equation of a line through a given point, and parallel to a given vector, derivation of cartesian form from vector form, equation of a line passing through two given points, the angle between two lines, the shortest distance between two lines, the distance between two skew lines, the distance between two parallel lines, the plane in cartesian form, equation of a plane in a normal form, equation of a plane passing through three non-collinear points, and much more. The chapter has three exercises and one miscellaneous exercise.


Chapter 12: Linear Programming



The chapter introduces you to Linear Programming and concepts that cover the topics of the mathematical formulation of the problem, graphical method of solving linear programming problems, different types of linear programming problems, and much more. The chapter has two exercises that focus on L.P. problems and other concepts.


Chapter 13: Probability



Probability deals with reviewing facts and formulas from the earlier class 11 chapter. The NCERT textbook for maths provides advanced concepts for several topics including conditional probability, properties of conditional probability, multiplication theorem on probability, multiplication rule of probability for more than two events, independent events, Baye’s theorem, the partition of a sample space, a theorem on total probability, random variables and its probability distributions, the probability distribution of a random variable, mean of the random variable, etc. The chapter has five exercises that help practice all the concepts and solutions for better exam preparation.


Why Eduauraa Maths Solutions NCERT Class 12?



Eduauraa provides a well-designed structure for your maths ncert solutions class 12. Our solutions are designed by the best teachers and academic experts using simple language and step-by-step solutions. Besides the solutions, we also include solved examples to provide efficient guidance to understand the concepts and utilize them in the examinations. With Eduauraa you can also get hold of a range of sample papers, assignments, exemplar questions, and previous year questions that make it easier for students to prepare themselves for their boards or engineering entrance examinations.

Latest Comments

Ramesh 5 Minutes ago

This is awesome explanation!

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Simple way to learn

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Simple way to learn

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Some frequently asked questions:

1

Is class 12 maths difficult?

Chemistry is one of the easiest subjects in the science stream. The subject will seem like a breeze once you study it with full concentration and consistency. It is important to read Chemistry every day. NCERT is the most important book for this purpose.

2

Is NCERT maths enough to score well?

As the syllabus is large, many students face problems in completing it in time. This causes problems in dedicating time to revision, especially for students who have not studied all the CBSE Class 12. It is important to have clear ideas and understandings of all the topics.

3

What are some tips for class 12 maths?

Some tips are as follows:

  • It is important to study every day and start early.

  • Understand each chapter rather than rushing through them.

  • Use reference books to gain a deeper understanding of the topics in NCERT.

  • Try and grasp the concepts and always ask questions.